Vacuum Expectation Value Research Articles

A model with light and heavy scalars in view of the effective theory

Abstract The low-energy effective potential for the model with a light scalar and a heavy scalar is derived. We perform the path integration for both heavy and light scalars and derive the low-energy effective potential in terms of only the light scalar. The effective potential is independent of the renormalization scale approximately. By setting the renormalization scale equal to the mass of the heavy scalar, one finds the corrections with the logarithm of the ratio of the two scalar masses. The large logarithm is summed with the renormalization group (RG), and the RG improved effective potential is derived. The improved effective potential includes the one-loop correction of the heavy scalar and the leading logarithmic corrections due to the light scalar. We study the correction to the vacuum expectation value of the light scalar and the dependence on the mass of the heavy scalar.

Integration of machine learning to increase steam turbine condenser vacuum and efficiency through gasket resealing and higher heat extraction into the atmosphere

In large thermal power facilities, thermal machines mainly fitted with steam turbines are used in thermodynamic process of converting thermal energy into mechanical work. In order to improve the efficiency of heat energy conversion into mechanical work, the increase of vacuum level in the condenser of a steam turbine was analyzed using the machine learning method. The vacuum in the steam turbine condenser increases after replacing the labyrinth gaskets with honeycomb ones, resealing the vacuum system and increasing the amount of cooling water through the condenser. The latter is controlled by algorithm, which is integrated into the steam turbine distribution control system. As a result of the increased vacuum in the steam turbine condenser, the enthalpy difference of the steam turbine low-pressure cylinder increases, and the steam turbine performs more mechanical work resulting in higher conversion efficiency. The drawback of the increased vacuum in the turbine condenser is that the flow of cooling water through the steam turbine condenser increases as well as heat dissipation from the condenser into the environment to be replaced by regenerative condensate heating. The results of the analysis show that the overall balance of the vacuum increase in the steam turbine condenser is positive, the steam turbine generates more power, and consequently the process efficiency increases by as much as 2.48 %.

Treating divergent perturbation theory: Lessons from exactly solvable 2D models at large N

We consider the operator product expansion (OPE) of correlation functions in the supersymmetric $O(N)$ non-linear sigma model at sub-leading order in the large $N$ limit in order to study the cancellation between ambiguities coming from infrared renormalons and those coming from various operators in the OPE. As has been discussed in the context of supersymmetric Yang-Mills theory in four dimensions, supersymmetry presents a challenge to this cancellation. In a bid to solve this problem we consider $O(N)$ as a toy model. A background field method inspired by Polyakov's treatment of the renormalization of the bosonic $O(N)$ model is used to identify explicit operators in the OPE of the two-point functions of bosonic and fermionic fields in the model. In order to identify the coefficient functions in the OPE, the exact two-point functions at sub-leading order in large $N$ are expanded in powers of the natural infrared length scale. The ambiguities arising from renormalons in the coefficient functions and vacuum expectation values of operators in the OPE are shown to cancel to all orders. The question of supersymmetric Yang-Mills theory without matter remains open.

Time-varying fine structure constant from naturally ultralight dark matter

We present a class of models in which the coupling of the photon to an ultralight scalar field that has a time-dependent vacuum expectation value causes the fine structure constant to oscillate in time. The scalar field is assumed to constitute all or part of the observed dark matter. Its mass is protected against radiative corrections by a discrete ${\mathbb{Z}}_{N}$ exchange symmetry that relates the Standard Model to several copies of itself. The abundance of dark matter is set by the misalignment mechanism. We show that the oscillations in the fine structure constant are large enough to be observed in current and near-future experiments.

Higgs-electroweak chiral Lagrangian: One-loop renormalization group equations

Starting from the one-loop divergences we obtained previously, we work out the renormalization of the Higgs-electroweak chiral Lagrangian explicitly and in detail. This includes the renormalization of the lowest-order Lagrangian, as well as the decomposition of the remaining divergences into a complete basis of next-to-leading-order counterterms. We provide the list of the corresponding beta functions. We show how our results match the one-loop renormalization of some of the dimension-6 operators in SMEFT. We further point out differences with related work in the literature and discuss them. As an application of the obtained results, we evaluate the divergences of the vacuum expectation value of the Higgs field at one loop and show that they can be appropriately removed by the corresponding renormalization. We also work out the finite renormalization required to keep the no-tadpole condition on the Higgs field at one loop.

Bumblebee field as a source of cosmological anisotropies

In this work, a bumblebee field is adopted in order to generate cosmological anisotropies. For that purpose, weassume a Bianchi I cosmology, as the background geometry, and a bumblebee field coupled to it.Bumblebee models are examples of a mechanism for the Lorentz symmetry violation byassuming a nonzero vacuum expectation value for the bumblebee field. When coupled tothe Bianchi I geometry, which is not in agreement with a cosmological principle, the bumblebee fieldplays the role of a source of anisotropies and produces a preferred axis. Thus, a fraction of the cosmic anisotropieswould come from the Lorentz symmetry violation.In the last part of the article, we try to assume an upper bound on the bumblebee field usingthe quadrupole and octopole moments of the cosmic microwave background radiation.

One-loop corrections to the Higgs boson invisible decay in the dark doublet phase of the N2HDM

The Higgs invisible decay width may soon become a powerful tool to probe extensions of the Standard Model with dark matter candidates at the Large Hadron Collider. In this work, we calculate the next-to-leading order (NLO) electroweak corrections to the 125 GeV Higgs decay width into two dark matter particles. The model is the next-to-minimal 2-Higgs-doublet model (N2HDM) in the dark doublet phase, that is, only one doublet and the singlet acquire vacuum expectation values. We show that the present measurement of the Higgs invisible branching ratio, BR(H → invisible < 0.11), does not lead to constraints on the parameter space of the model at leading order. This is due to the very precise measurements of the Higgs couplings but could change in the near future. Furthermore, if NLO corrections are required not to be unphysically large, no limits on the parameter space can be extracted from the NLO results.

Exploring multi-Higgs models with softly broken large discrete symmetry groups

We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically, proliferation of quadratic couplings in the most general softly broken case makes the analysis cumbersome. We identify two sets of soft breaking terms which play different roles: those which preserve the symmetric vacuum expectation value alignment, and the remaining terms which shift it. Focusing on alignment preserving terms, we check which structural features of the symmetric parent model are conserved and which are modified. We find remarkable examples of structural features which are inherited from the parent symmetric model and which persist even when no exact symmetry is left. The general procedure is illustrated with the example of the three-Higgs-doublet model with the softly broken symmetry group Sigma (36).

Linearized supergravity with a dynamical preferred frame

We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field called aether. Embedding aether into a chiral vector superfield, we construct the most general action which describes dynamics of linear perturbations around the Lorentz-violating vacuum and is invariant under the linearized supergravity transformations. The analysis is performed both in the off-shell non-minimal superfield formulation of supergravity and in the “on-shell” approach invoking only physical component fields. The resulting model contains a single free coupling, in addition to the standard supergravity parameters. The spectrum of physical excitations features an enhanced on-shell gravity multiplet comprising four states with helicities 2, 3/2, 3/2 and 1 propagating with superluminal velocity. The remaining excitations propagate with the speed of light. We outline the observational constraints on the model following from its low-energy phenomenology.

The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem

The content of two additional Ward identities exhibited by the U(1) Higgs model is exploited. These novel Ward identities can be derived only when a pair of local composite operators providing a gauge invariant setup for the Higgs particle and the massive vector boson is introduced in the theory from the beginning. Among the results obtained from the above mentioned Ward identities, we underline a new exact relationship between the stationary condition for the vacuum energy, the vanishing of the tadpoles and the vacuum expectation value of the gauge invariant scalar operator. We also present a characterization of the two-point correlation function of the composite operator corresponding to the vector boson in terms of the two-point function of the elementary gauge fields. Finally, a discussion on the connection between the cartesian and the polar parametrization of the complex scalar field is presented in the light of the Equivalence Theorem. The latter can in the current case be understood in the language of a constrained cohomology, which also allows to rewrite the action in terms of the aforementioned gauge invariant operators. We also comment on the diminished role of the global U(1) symmetry and its breaking.

Casimir densities induced by a sphere in the hyperbolic vacuum of de Sitter spacetime

Complete set of modes and the Hadamard function are constructed for a scalar field inside and outside a sphere in (D+1)-dimensional de Sitter spacetime foliated by negative constant curvature spaces. We assume that the field obeys Robin boundary condition on the sphere. The contributions in the Hadamard function induced by the sphere are explicitly separated and the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor are investigated for the hyperbolic vacuum. In the flat spacetime limit the latter is reduced to the conformal vacuum in the Milne universe and is different from the maximally symmetric Bunch-Davies vacuum state. The vacuum energy-momentum tensor has a nonzero off-diagonal component that describes the energy flux in the radial direction. The latter is a purely sphere-induced effect and is absent in the boundary-free geometry. Depending on the constant in Robin boundary condition and also on the radial coordinate, the energy flux can be directed either from the sphere or towards the sphere. At early stages of the cosmological expansion the effects of the spacetime curvature on the sphere-induced VEVs are weak and the leading terms in the corresponding expansions coincide with those for a sphere in the Milne universe. The influence of the gravitational field is essential at late stages of the expansion. Depending on the field mass and the curvature coupling parameter, the decay of the sphere-induced VEVs, as functions of the time coordinate, is monotonic or damping oscillatory. At large distances from the sphere the fall-off of the sphere-induced VEVs, as functions of the geodesic distance, is exponential for both massless and massive fields.

A modified version of the Koide formula from flavor nonets in a scalar potential model and in a Yukawaon model

We present a modified version of the Koide formula from a scalar potential model or from a Yukawaon model, based on scalar fields set up in a nonet representation of the SU(3) flavor symmetry in the Standard Model. The Koide's character, which involves the Standard Model fermion mass ratios, is derived from the vacuum expectation value of the nonet field in either model. The scalar potential in the scalar potential model or the superpotential in the Yukawaon model is constructed with all terms invariant under symmetries. The resulting Koide's character, which is modified by two effective parameters, can fit the experimental mass data of charged leptons, up quarks and down quarks. It offers a natural interpretation of the Standard Model fermion mass spectrum.

$SU(5)_{L} \times U(1)_{Y}$ electroweak unification

Abstract We propose here—for the first time in the literature, to our best knowledge—an electroweak unification based on the $SU(5)_{L}\times U(1)_{Y}$ gauge group. The spontaneous symmetry breaking takes place in the manner $SU(5)_{L}\times U(1)_{Y} \rightarrow U(1)_{em}$, due to a particular Higgs sector consisting of five scalar quintuplets. Each scalar quintuplet acquires its own vacuum expectation value, by means of a proper parametrization which is worked out once an overall vacuum expectation value in the model is established. The decoupling of the low-energy regime (corresponding to the Standard Model) from the high scale (required by our model here) is straightforwardly achieved in order to preserve the consistency with the present experimental data. Finally, a promising phenomenological outcome is derived by simply tuning a single free parameter. Our results also include, besides a viable one-parameter mass spectrum, the prediction of precisely three generations in the fermion sector and the electric charge quantization.

Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Traversable wormhole solution with a background Kalb–Ramond field

We obtain a static spherically symmetric wormhole solution due to the vacuum expectation value (vev) of a Kalb–Ramond field. The Kalb–Ramond (vev) is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb–Ramond (vev) and the Ricci tensor, we found an exact traversable wormhole solution sustained by matter sources with a negative isotropic pressure. The matter source satisfies the energy conditions at the throat for particular choices of the LSB parameter. Moreover, we employ the Gauss–Bonnet method to analyze the deflection angle of light in the weak limit approximation.

Scale symmetry breaking, quantum anomalous energy and proton mass decomposition

We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales. We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition. We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks. We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.

Radiative interactions between new non-Abelian gauge sector and the standard model

We discuss one loop generation of the term connecting gauge fields from a local hidden SU(2)H and the standard model U(1)Y introducing an SU(2)H doublet fermion with non-zero hypercharge and a scalar field in adjoint representation. Then we obtain a kinetic mixing term between SU(2)H and U(1)Y gauge fields after the adjoint scalar field developing vacuum expectation value. We illustrate such a concrete scenario introducing a dark matter model in an ultraviolet (UV) completion with local SU(2)H symmetry where the scalar doublet is our dark matter candidate and its stability is guaranteed by remnant Z2 symmetry from SU(2)H. Relic density of dark matter is calculated focusing on the case in which dark matter annihilate into known particles via SU(2)H gauge interactions with radiatively induced kinetic mixing.

Confronting the magnetically-induced holographic composite inflation with observation

We study the observational predictions of the phenomenological anti-de Sitter (AdS)/QCD inspired model, in which the inflaton field emerges in a four-dimensional strongly coupled gauge theory, in which the chiral symmetry breaking occurs through the formation of the quark condensate. Based on a top-down approach of AdS/QCD, using a D7-brane in the background of ${N}_{c}$ D3-branes, it has already been shown that chiral symmetry breaking in a magnetic field through the generation of the Higgs vacuum expectation value could be a second-order phase transition, although it was doubted that this scenario could lead to enough inflation. Using an iterative method, we consistently solve for the time-dependent parameters, including the embedding function of the D7-brane and the Hubble parameter of the expanding background. We show that with ${N}_{c}\ensuremath{\sim}{10}^{7}$ and ${g}_{\mathrm{UV}}\ensuremath{\sim}\mathrm{few}\ifmmode\times\else\texttimes\fi{}0.1$, the predictions of the inflationary model are consistent with the most stringent constraints placed on the inflationary models by Planck 2018. Although the model is capable of producing a large amount of gravitational waves, $r\ensuremath{\simeq}0.01$, the displacement of the canonical mass dimension-1 scalar field remains below the Planck mass, in violation of the Lyth bound.

Vacuum stability vs. positivity in real singlet scalar extension of the standard model

We assume a generic real singlet scalar extension of the Standard Model living in the vacuum (v,w) at the electroweak scale with v=246 GeV and w being respectively the Higgs and the singlet scalar vacuum expectation values. By requiring absolute vacuum stability for the vacuum (v,w), the positivity condition and the perturbativity up to the Planck scale, we show that the viable space of parameters in the model is strongly constrained for various singlet scalar vacuum expectation values w=0.1,1,10,100 TeV. Also, it turns out that the singlet scalar mass can be from a few GeV up to less than TeV.

Gravitational origin of dark matter and Majorana neutrino mass with non-minimal quartic inflation

We propose a minimal framework to address successful quartic inflation, dark matter (DM) production in the early universe and non-vanishing tiny Majorana neutrino mass from a common gravitational origin point of view. In this setup, the quartic inflation is revived successfully via non-minimal coupling of inflaton to gravity while the production of DM takes place from purely gravitational effects through a misalignment mechanism. The generation of light Majorana neutrino mass is aided by explicit breaking of global lepton number symmetry through Planck suppressed operators involving non-zero vacuum expectation value (VEV) of the inflaton field. We present a detailed study of the DM yield in presence of non-minimal inflation, considering both the metric and the Palatini formalisms of gravity wherever appropriate. We reach at some interesting and different results in the DM sector compared to the earlier works in the similar direction with minimal inflationary background. Restricting to the light DM regime ( O ( 1 ) keV- O ( 100 ) MeV ) where classical production is expected to dominate over the quantum production, we numerically predict the DM mass by varying the DM quartic and non-minimal coupling, to be consistent with relic density requirements. We also obtain some non-trivial dependence of DM phenomenology on some of the relevant parameters of the inflation sector e.g. non minimal coupling and inflaton VEV. To explore the dependence on inflationary parameters further, we also estimate the DM relic using the same mechanism for two other inflationary models consistent with latest data and observe that one of these models predicts different range of DM mass up to hundreds of TeV.